In high field MRI, the SNR is significantly increased and makes possible to improve the voxel resolution. A high number of data's can be acquired on the patient and should help his diagnosis by the physician. The timing restriction to scan the patient is an obligation in the medical institutions. Getting a high resolution with a limited time scan is a real challenge in MRI reconstruction. Also, high rf stimulation and gradient amplitudes are restricted in high field MRI to avoid nerves stimulation. These constraints make harder the sampling and the acquisition of data's. The sampling of data's in MRI coupled to the MRI reconstruction is a key point and its interest is growing with the presence of high field MRI. In this ISPS, a well-known approach of convex optimization by minimizing Total-Variation norm will be presented in the case of MRI reconstruction. Simulation of data's and real phantoms acquired on the 11.7 T MRI scan will be presented.